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{'Lhash': '569452284045574238800045226039,1740203176837685628075136630996,2387614388192443413895697943016,3375220341406421048487562227522', 'a10': 0, 'a2': 3, 'a3': -2, 'a4': 3, 'a5': 0, 'a6': -6, 'a7': -6, 'a8': 0, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.356744149402594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [13, [1, 4, 30, 52, 169]]], 'bad_primes': [5, 13], 'central_character': '325.1', 'coefficient_field': '1.1.1.1', 'conductor': 11156640625, 'conductor_radical': 65, 'degree': 8, 'euler_factors': [[1, -3, 6, -9, 11, -18, 24, -24, 16], [1, 2, -3, 2, 28, 6, -27, 54, 81], [1], [1, 6, 29, 102, 324, 714, 1421, 2058, 2401], [1, 0, 15, 0, 104, 0, 1815, 0, 14641], [1, 4, 30, 52, 169], [1, 0, -13, 0, -120, 0, -3757, 0, 83521], [1, -6, 53, -246, 1548, -4674, 19133, -41154, 130321], [1, 0, -25, 0, 96, 0, -13225, 0, 279841], [1, 0, -37, 0, 528, 0, -31117, 0, 707281], [1, 0, 8, 0, 1182, 0, 7688, 0, 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'11.97387849940462873845815874446575'], 'prelabel': '8-325e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.610943222367447, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1587463167307226964, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44921864427236443265723462774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.37277825334865716856496814071', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.88349564758820319220848150770', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 45.356744149402594, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 11156640625, 'conductor_radical': 65, 'degree': 8, 'dirichlet_coefficients': [1, 3, -2, 3, 0, -6, -6, 0, 7, 0, 0, -6, -4, -18, 0, -2, 0, 21, 6, 0, 12, 0, 0, 0, 0, -12, -22, -18, 0, 0, 0, 6, 0, 0, 0, 21, 0, 18, 8, 0, 0, 36, -12, 0, 0, 0, 0, 4, 7, 0, 0, -12, 12, -66, 0, 0, -12, 0, 30, 0, 12, 0, -42, 27, 0, 0, -24, 0, 0, 0, 6, 0, 0, 0, 0, 18, 0, 24, -24, 0, 41, 0, 0, 36, 0, -36, 0, 0, -24, 0, 24, 0, 0, 0, 0, -12, -12, 21, 0, 0], 'euler11': [1, 0, 15, 0, 104, 0, 1815, 0, 14641], 'euler13': [1, 4, 30, 52, 169, 0, 0, 0, 0], 'euler17': [1, 0, -13, 0, -120, 0, -3757, 0, 83521], 'euler19': [1, -6, 53, -246, 1548, -4674, 19133, -41154, 130321], 'euler2': [1, -3, 6, -9, 11, -18, 24, -24, 16], 'euler23': [1, 0, -25, 0, 96, 0, -13225, 0, 279841], 'euler29': [1, 0, -37, 0, 528, 0, -31117, 0, 707281], 'euler3': [1, 2, -3, 2, 28, 6, -27, 54, 81], 'euler31': [1, 0, 8, 0, 1182, 0, 7688, 0, 923521], 'euler37': [1, 0, 11, 0, -1248, 0, 15059, 0, 1874161], 'euler41': [1, 0, 75, 0, 3944, 0, 126075, 0, 2825761], 'euler43': [1, 12, 43, 180, 2160, 7740, 79507, 954084, 3418801], 'euler47': [1, 0, -108, 0, 5990, 0, -238572, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -12, 224, -1764, 18270, -93492, 629216, -1786524, 7890481], 'euler59': [1, -30, 465, -4950, 41444, -292050, 1618665, -6161370, 12117361], 'euler61': [1, -12, 7, -180, 6264, -10980, 26047, -2723772, 13845841], 'euler67': [1, 24, 311, 2856, 22536, 191352, 1396079, 7218312, 20151121], 'euler7': [1, 6, 29, 102, 324, 714, 1421, 2058, 2401], 'euler71': [1, -6, 129, -702, 9500, -49842, 650289, -2147466, 25411681], 'euler73': [1, 0, -292, 0, 31974, 0, -1556068, 0, 28398241], 'euler79': [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], 'euler83': [1, 0, -168, 0, 18734, 0, -1157352, 0, 47458321], 'euler89': [1, 24, 411, 5256, 57128, 467784, 3255531, 16919256, 62742241], 'euler97': [1, 12, 191, 1716, 15696, 166452, 1797119, 10952076, 88529281], 'euler_factors': [[1, -3, 6, -9, 11, -18, 24, -24, 16], [1, 2, -3, 2, 28, 6, -27, 54, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, 29, 102, 324, 714, 1421, 2058, 2401], [1, 0, 15, 0, 104, 0, 1815, 0, 14641], [1, 4, 30, 52, 169, 0, 0, 0, 0], [1, 0, -13, 0, -120, 0, -3757, 0, 83521], [1, -6, 53, -246, 1548, -4674, 19133, -41154, 130321], [1, 0, -25, 0, 96, 0, -13225, 0, 279841], [1, 0, -37, 0, 528, 0, -31117, 0, 707281], [1, 0, 8, 0, 1182, 0, 7688, 0, 923521], [1, 0, 11, 0, -1248, 0, 15059, 0, 1874161], [1, 0, 75, 0, 3944, 0, 126075, 0, 2825761], [1, 12, 43, 180, 2160, 7740, 79507, 954084, 3418801], [1, 0, -108, 0, 5990, 0, -238572, 0, 4879681], [1, -12, 224, -1764, 18270, -93492, 629216, -1786524, 7890481], [1, -30, 465, -4950, 41444, -292050, 1618665, -6161370, 12117361], [1, -12, 7, -180, 6264, -10980, 26047, -2723772, 13845841], [1, 24, 311, 2856, 22536, 191352, 1396079, 7218312, 20151121], [1, -6, 129, -702, 9500, -49842, 650289, -2147466, 25411681], [1, 0, -292, 0, 31974, 0, -1556068, 0, 28398241], [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], [1, 0, -168, 0, 18734, 0, -1157352, 0, 47458321], [1, 24, 411, 5256, 57128, 467784, 3255531, 16919256, 62742241], [1, 12, 191, 1716, 15696, 166452, 1797119, 10952076, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/2/n/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-325e4-1.1-c1e4-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-325e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.610943222367447, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1587463167307226964, 'z1': {'__RealLiteral__': 0, 'data': '0.44921864427236443265723462774', 'prec': 103}}
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{'Lhash': '569452284045574238800045226039,1740203176837685628075136630996,2387614388192443413895697943016,3375220341406421048487562227522', 'Lhash_array': ['569452284045574238800045226039', '1740203176837685628075136630996', '2387614388192443413895697943016', '3375220341406421048487562227522'], 'label': '8-325e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/2/n/c'}